Fact 2.2 [1]} 
Suppose that \(f \in \Gamma _{0} (\mathcal {H}) \)  with \(\operatorname{int}\operatorname{dom}f \ne \varnothing \) , that \(f\)  is Gâteaux differentiable on \(\operatorname{int}\operatorname{dom}f\) , and that \(f\)  is essentially strictly convex.
Let \(x\)  and \(y\)  be in \( \operatorname{int}\operatorname{dom}f\) . Then \(D_{f}(x, y) = D_{f^{*}}(\nabla f (y),\nabla f (x))\) .

